The purpose of this project is to improve the remission induction rate of acute lymphocytic leukemia in adult patients utilizing vincristine and dexamethasone with intermittent moderate doses of methotrexate followed by L'asparaginase. A second objective is to decrease the incidence of severe infections during induction therapy by utilizing oral nonabsorbable antibiotics. A third objective is to determine whether intermittent high dose methotrexate with leucovorin rescue and with vincristine and dexamethasone will prolong remission duration. The fourth objective is to determine the efficacy of moderate and high dose methotrexate in preventing meningeal leukemia and to correlate the clinical effectiveness with the cerebrospinal fluid methotrexate levels. To date 25 patients have been entered onto this study. Fourteen patients had no prior treatment, eleven had prior treatment. For the no prior treatment patients, six patients are still on study and eight are off study. For the prior treatment patients, five patients are still on study and six patients are off study. For the no prior treatment patients, complete remissions have been achieved in nine of fourteen patients that went through induction. One patient is too early to evaluate. For the prior treatment patients, eight patients achieved complete remission.